Problem: Solve for $x$ and $y$ using elimination. ${6x+y = 50}$ ${5x-y = 38}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $11x = 88$ $\dfrac{11x}{{11}} = \dfrac{88}{{11}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {6x+y = 50}\thinspace$ to find $y$ ${6}{(8)}{ + y = 50}$ $48+y = 50$ $48{-48} + y = 50{-48}$ ${y = 2}$ You can also plug ${x = 8}$ into $\thinspace {5x-y = 38}\thinspace$ and get the same answer for $y$ : ${5}{(8)}{ - y = 38}$ ${y = 2}$